My problem is in the last line above. There's still an h remaining. Why didn't it get replaced? If I could properly replace it, I can then take one more step and solve this related rates problem by solving for Dt[h].

Wow, your awesome; you went above and beyond my expectations, I love you. You answered the question, improved my PoC to a legit answer, showed me a more idiomatic concise way of solving problems such as these, and then you answered my original query even though I was actually asking more, and I didn't even realize it.
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Adam DreaverJan 25 '13 at 8:13

@AdamDreaver Well, I have to confess: I'm green, I've blue feathers attached to my ears, and I don't speak, but growl. Do you still love me?
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belisariusJan 25 '13 at 8:30

@AdamDreaver And let me say that we need more curious students like you lurking on this site
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belisariusJan 25 '13 at 8:32

I'd still love you if were a rock; you're so amazing I could just make a multiple choice question and answer and I bet you would break symmetry and roll onto the right answer; that's how much you rock!
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Adam DreaverJan 25 '13 at 8:40

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